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采用间接边界元法研究了层状半空间中凹陷地形对斜入射平面P波的2.5维散射问题。取无限长凹陷地形任一横截面,将边界以斜线单元离散,通过自由场反应分析,求得假想边界上各单元的应力响应。施加虚拟移动均布斜线荷载,求得应力格林函数。根据凹陷边界上的零应力边界条件确定虚拟移动均布斜线荷载密度,将自由场响应和虚拟移动均布斜线荷载产生的响应叠加起来,即得到问题的解答。通过与已有结果的对比,验证了本文方法的正确性。最后,以均匀弹性半空间和基岩上单一土层中凹陷地形对斜入射平面P波的2.5维散射为例,进行了数值计算分析,结果表明:凹陷地形的2.5维散射和二维散射之间存在明显差异;层状半空间中凹陷地形和均匀半空间中凹陷地形对波的散射作用存在显著差别。分析了造成差别的原因,并深入讨论了入射角度、覆盖层厚度和刚度对散射作用的影响。
The indirect boundary element method is used to study the 2.5-D scattering problem of the concave topography on the oblique incident plane P wave in the layered half-space. Take any cross-section of indefinite long depression topography, divide the boundary by slant-line elements and obtain the stress response of each element on the imaginary boundary through free-field reaction analysis. Applying a virtual moving uniform diagonal load to find the stress Green’s function. According to the zero stress boundary condition on the sag boundary, the uniform moving diagonal load density is determined, and the responses of the free-field response and the virtual moving uniform diagonal load are summed to obtain the solution of the problem. By comparing with the existing results, the correctness of this method is verified. Finally, taking the 2.5 -dimensional scattering of the obliquely incident plane P waves in a homogeneous elastic half-space and a single soil layer on a bedrock as an example, the numerical calculation and analysis are carried out. The results show that the 2.5-D scattering and the two-dimensional scattering of the depression topography There is a significant difference between them; the difference between the concave topography in the layered half-space and the concave topography in the uniform half- The causes of the differences are analyzed, and the effects of incident angle, thickness and stiffness of the coating on scattering are discussed in depth.