流体饱和半空间二维地形三分量弹性波散射间接边界元模拟  

IBEM simulation of three-component scattering of elastic waves in a fluid-saturated half-space with 2D topography

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 Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin 300350,China;Department of Civil Engineering,Tianjin University,Tianjin 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：《地球物理学报》2021年第8期2766-2779,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(51778413,51578373);天津市研究生科研创新项目(2019YJSB176)资助.

摘　　要：无限长局部地形地震波斜入射响应问题称为二维三分量问题,在计算量远小于三维的情况下,一定程度上反映了近地表场地的三维动力响应特征.基于天然土体的成层性及固液两相耦合特性,以层状多孔介质内部移动线荷载(孔隙水压)动力格林函数作为基本解,开展流体饱和半空间二维地形三分量弹性波散射的2.5维间接边界元模拟研究.总场响应由自由波场和散射波场叠加构成,前者可由直接刚度法求得,后者则通过施加移动虚拟均布荷载和移动虚拟孔隙水压所产生的动力响应来模拟.该方法优势在于离散仅限于地形底边界(无须离散自由地表),格林函数计算不存在奇异性(荷载可直接加在边界上),容易控制计算精度,对复杂边界条件具有很强的适应性.在退化验证和精度比较的基础上,以梯形凹陷和半椭圆沉积地形为例,模拟了时域和频域的流体饱和半空间三维弹性波散射响应.研究表明:局部地形的地震动响应依赖于入射频率、入射角度、边界透水条件、土层刚度和土层厚度等,入射波、反射波和散射波相互干涉,极大延长了位移的振动持续时间.Seismic response of infinite local geometry subjected to obliquely incident waves is called a 2-D three-component problem,which reflects the 3D dynamic response characteristics of the near-surface site to some extent under the premise that calculation amount is much less than a 3D case.Considering the stratification and solid-liquid coupling properties of natural soil,a 2.5D IBEM(indirect boundary element method)is used to solve three-component scattering in a fluid-saturated,poroelastic layered half-space with 2D topography.In this IBEM dynamic the Green functions are used for moving forces(pore pressure)acting on an internal inclined line as its fundamental solutions.In the calculation,the total wave fields are decomposed into a free field and a scattered field,the former can be determined by the direct stiffness method,and the latter is simulated by the dynamic response of a moving fictitious distributed load as well as fictitious moving pore pressure applied to each discrete inclined line element.The advantage of this IBEM is that the discretization is only confined to the geometry boundary(no need to discretize the free surface),and no singularity in the calculation of Green's function(the load can be directly applied to the boundary),so it is easy to meet the calculation accuracy and complex boundary conditions.On the basis of degradation verification and precision comparison,taking a trapezoidal canyon and semi-elliptical valley as examples,the scattering effect of 3-D elastic waves in fluid-saturated half-space both in the frequency and time domains is simulated.The results show that the earthquake ground motion of the local topography depends on the incident frequency,incident angle,boundary drainage condition,soil layer stiffness and soil layer thickness.Due to the existence of topography,incident,reflected and scattered waves interfere with each other,which greatly prolongs the vibration duration of displacement.

关 键 词：流体饱和半空间 地震波传播 二维三分量 边界元法 移动线源 

分 类 号：P315[天文地球—地震学]