局部复杂场地Rayleigh波传播特性分析的SBFEM模型研究

基于土-结构动力相互作用（SSI）的原理，将求解包含局部复杂地形的散射场问题，分解为规则开挖场地的动刚度、包含复杂构造散射体的动刚度和自由场波动输入3个问题的求解，并依据子结构控制方程，提出了一种高精度的比例边界有限（SBFEM）计算模型。通过计算半圆形河谷和半圆形沉积河谷两个算例，验证了SBFEM计算模型的正确性。较为系统地讨论了矩形峡谷、垂直断层和孤凸山体等常见复杂地形对Rayleigh波场的散射作用。结果表明：峡谷深度、软弱断层破碎带和孤凸山体对Rayleigh波都有一定阻挡作用；峡谷宽度、断层宽度和硬性断层填充物等因素对Rayleigh波散射作用影响不明显。SBFEM分析模型可应用于隔震沟、隔震帷幕设计，对大坝、桥梁等工程的选址提供有益的建议。

Research on influence of partial terrain to scattering of Rayleigh wave based on SBFEM

This paper is focused on scattering and diffraction of Rayleigh wave caused by local topographies. For this purpose, a substructure replacement technique based on the theory of soil-structure interaction is used to evaluate the effects of canyon, vertical fault fracture zones and mountains on scattering and diffraction of Rayleigh wave. Based on the substructure theory, the scattering problem is decomposed into three parts: solving the dynamic stiffness of the ground of excavation, solving the dynamic stiffness of the complex structure and solving the input wave of the free field. The dynamic stiffness of the ground of excavation and the complex structure are solved using scaled boundary finite element method (SBFEM). In order to validate the proposed method, two examples are solved and the results are in good agreement with those reported in the literature. Then the scattering of Rayleigh waves by a variety of complex terrains, such as canyons, vertical faults and mountains are analyzed. Numerical results are presented in graphical form for the surface displacement and displacement spectra. Conclusions in this study can be useful in engineering practice. The proposed method can be applied to the design of seismic isolation ditch and seismic adaptability analysis of dam and bridge.