层状半空间中周期分布凸起地形对平面SH波的散射

Scattering and diffraction of plane SH-waves by periodically distributed hill topographies

提出了一种新的以层状半空间中周期分布斜线荷载动力格林函数为基本解的间接边界元方法,研究了周期分布凸起地形对平面SH波的散射问题.方法将散射波场分解为凸起内部散射波场和凸起外部散射波场.凸起内部散射波场通过在凸起闭合边界上施加虚拟斜线荷载产生的动力响应来模拟,而凸起外部散射波场则通过在凸起与半空间交界面上施加虚拟周期分布斜线荷载产生的动力响应来模拟.周期分布斜线荷载动力格林函数的引入,使得本文方法仅需针对一个凸起进行边界单元的离散和求解,便可完成问题的求解,避免了通过截断无限边界求解而引入的误差,方法具有较高精度的同时显著降低了求解自由度.文中通过与已有结果的比较,验证了方法的正确性,并以均匀半空间和基岩上单一土层中周期分布凸起为例进行了数值计算分析.研究表明,凸起间距对凸起地形间的动力相互作用有着显著的影响,同时层状半空间中周期分布凸起地形对SH波的散射与均匀半空间情况也有着显著的差别.

In this paper, a new method is adopted to study the scattering and diffraction of plane SH-waves by periodically distributed hills in a layered half-space. In this method, the indirect boundary element method with the combination of Green＇s functions of uniformly distributed loads acting on periodically distributed inclined lines is employed. The whole region is decomposed into the closed hill region and opened layered half-space region. The simulation of scattered field in the hill region is performed by dynamic response of virtual loads acting on inclined lines on the closed hill boundary, while the scattered field in the opened layered halfspace region by dynamic response of virtual uniformly distributed loads acting on periodically distributed inclined lines on the boundary between the hill and the half-space. The periodicity feature of the hills is exploited to limit the discretization effort to a single hill, which avoids errors induced by the truncation of the infinite boundary, and thus high accuracy is achieved and the demand of memory can be reduced greatly. The accuracy of the method is verified by comparison with published results. Periodically distributed semi circular hills in a homogenous half-space and a single soil layer on bed rock are utilized as an example for parametric studies. Quite obvious difference could be found between the numerical results of the dynamic responses of periodically distributed hills and those for a single hill. The existence of distinct dynamic interactions between the hills should also be highlighted.