Dynamic analysis for shallow buried circular inclusion impacted by SH-wave in a softlayered half-space
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摘要: 利用复变函数法和波函数展开法, 对地表软覆盖层中浅埋圆形夹杂在稳态SH波作用下的动应力集中问题进行研究并给出了解析解。根据SH波散射时的衰减特性, 采用了大圆弧假定的方法, 将半空间覆盖层直线边界问题转化为曲面边界问题。通过算例分析了SH波垂直入射时, 不同入射波波数和圆夹杂与半空间的波数比对圆形夹杂周边动应力集中因子的分布和动应力集中因子最大值变化的影响。算例表明, 圆形夹杂越“软”, 其波数越大, 夹杂周边的动应力集中因子越大; 入射波波数约0.35时, 夹杂周边的最大动应力集中因子达到最大值。Abstract: In this study, we investigated the dynamic stress concentration factor of single circular inclusion shallow buried in surface softlayered half space impacted by steady SH-wave using the complex variable function method and the wave function expansion method, and obtained the analytical solution. Based on the attenuation characteristic of SH-Wave scattering and using the large-arc assumption method, we converted the problem of the layer half space linear boundary to that of the circle boundary and, by an example, analyzed the influence of different incident wave numbers and the ratios of the circular inclusion to the half space on the distribution of the dynamic stress concentration factor and on the change of the maximum dynamic stress concentration when the incident SH-wave is vertical. Numerical examples show that the "softer" the circular inclusion, the greater its wave number of circular inclusions, and the larger the dynamic stress concentration factor around the circular inclusion; the maximum dynamic stress concentration factor around circular inclusion reaches its maximum value when the number of the incident SH-wave approaches 0.35.
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图 1 地表覆盖层及半空间问题模型示意图
Figure 1. Schematic diagram of the layer half space and the half space model
图 2 ρ*=G*=k*=k#=1时圆形夹杂边的动应力集中因子Kd
Figure 2. Kd around circular inclusion (ρ*=G*=k*=k#=1)
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