无破碎带断层场地对SH波的散射

Scattering of Plane SH-waves by a Fault Site without a Fracture Zone

摘要:

在层状半空间精确动力刚度矩阵和斜线荷载动力格林函数的基础上建立间接边界元方法,在频域内求解无破碎带断层场地对入射平面SH波的散射。为方便求解,将总波场分解为自由波场和散射波场,自由波场由直接刚度法求得,断层两侧的散射波场通过在断层面上分别对两侧施加均布斜线荷载产生的动力响应来模拟,虚拟荷载的密度可通过引入断层表面的边界条件确定,最后叠加自由波场和散射波场求得总波场。以有落差断层和无落差断层模型为例进行数值计算,分析断层落差、断层倾角以及断层两侧介质的刚度比对散射效应的影响。研究表明,断层落差与波长相当时,断层对SH波的放大作用最大;地表位移幅值随着断层倾角的增大逐渐增大;若断层无落差且其两侧刚度不同时,一般刚度较小一侧地表位移幅值较大且振荡更为剧烈,波从刚度较小一侧入射时位移幅值放大尤为显著。

Abstract:

Based on the exact dynamic stiffness matrix of a layered half-space and Green's functions for a uniformly distributed load acting on an inclined line, an indirect boundary element method(IBEM) is proposed. The wave scattering of plane SH-waves by a fault site without a fracture zone is studied using the proposed IBEM. The total wave fields are decomposed into the free and scattered fields to facilitate calculation. The free fields are determined by the direct stiffness method, and the scattered fields located in the regions above and below the fault are simulated by applying two sets of uniformly distributed loads on the surface of the fault. The densities of the two sets of virtual loads can be determined by introducing the boundary conditions on the surface of the fault(zero-stress condition and continuity conditions of displacement and stress). Finally, the total dynamic responses are obtained by adding the free fields to the scattered fields. The implications of the method are described in detail, including the size of the boundary element and the integration sample. Further, numerical calculations are performed using fault sites with and without fall heights as examples, and the effects of fall height, inclined angle of the fault, and the shear stiffness modulus ratio between the materials on the two sides of the fault are analyzed. Numerical results show that the largest displacement amplitudes are expected when the fall height approaches the shear wavelength of the incident SH-waves. The amplitudes of the displacement gradually increase with increases in the inclined angle of the fault. Generally, the displacement amplitudes are much larger with variations that are much more complex on the softer side of the fault when the stiffness modulus of two sides differs; moreover, the displacement amplitudes can be especially large when SH-waves are incident from the softer side of the fault site.